How to solve a set of Linear equations?

Question

I need to solve a system of linear equations:

aQ + bP = c
dQ + eP = f

Where:

a ~ N(100;10)
b ~ N(-1;0.1)
c ~ N(10;1)
d ~ N(10;0         


        

Answer 1

You could try using apply()

# data  
df = data.frame(a,b,c,d,e,f)

# apply function
out = t(apply(df, 1, 
      function(x){ 
      coefs = matrix( c(x['a'], x['d'], x['b'], x['e']), 2, 2); 
      ys = array(c(x['c'],x['f']),2); 
      out = solve(coefs, ys); 
      names(out) = c('P','Q');
      out}))

Or else using sapply()

out = t(sapply(seq(100), function(i){
       coefs = matrix(c(a[i], d[i], b[i] ,e[i]),2,2); ys = array(c(c[i],f[i]),2);
       out = solve(coefs, ys); names(out) = c('P','Q'); 
       out}))

and if you want to use for loop, here is what you could do

# declare matrix to store the output
out = matrix(ncol=2, nrow=100) 

# populate declared matrix using for loop
for(i in 1:100){  
    coefs = matrix(c(a[i],d[i],b[i],e[i]),2,2)
    ys = array(c(c[i],f[i]),2)
    out[i,] = as.vector(solve(coefs, ys))
    colnames(out) = c('P','Q')
    out}